Related papers: L-systems with Multiplication Operator and c-Entro…
Given a categorical dynamical system, i.e. a triangulated category together with an endofunctor, one can try to understand the complexity of the system by computing the entropy of the endofunctor. Computing the entropy of the composition of…
This work includes a number of novel contributions for the multiple-source adaptation problem. We present new normalized solutions with strong theoretical guarantees for the cross-entropy loss and other similar losses. We also provide new…
We present a new method to transform an expanded class of non-selfadjoint advection-diffusion operators into self-adjoint operators. The transform is based on a combination of a point transform and Lie transform in conjunction with an…
The shear shallow water model is an extension of the classical shallow water model to include the effects of vertical shear. It is a system of six non-linear hyperbolic PDE with non-conservative products. We develop a high-order entropy…
Entropy principles based on thermodynamic consistency requirements are widely used for constitutive modeling in continuum mechanics, providing physical constraints on a priori unknown constitutive functions. The well-known M\"uller-Liu…
We explore analytically and numerically agglomeration driven by advection and localized source. The system is inhomogeneous in one dimension, viz. along the direction of advection. We analyze a simplified model with mass-independent…
We study the energy transfer in the linear system $$ \begin{cases} \ddot u+u+\dot u=b\dot v\\ \ddot v+v-\epsilon \dot v=-b\dot u \end{cases} $$ made by two coupled differential equations, the first one dissipative and the second one…
Many complex systems are characterized by non-Boltzmann distribution functions of their statistical variables. If one wants to -- justified or not -- hold on to the maximum entropy principle for complex statistical systems (non-Boltzmann)…
Pairs of pseudoscalar neutral mesons from decays of vector resonances are studied as bipartite systems in the framework of density operator. Time-dependent quantum entanglement is quantified in terms of the entanglement entropy and these…
The asymptotic restriction problem for tensors can be reduced to finding all parameters that are normalized, monotone under restrictions, additive under direct sums and multiplicative under tensor products, the simplest of which are the…
Copula Entropy (CE) is a recently introduced concept for measuring correlation/dependence in information theory. In this paper, the theory of CE is introduced and the thermodynamic interpretation of CE is presented with N-particle…
The scaling of entanglement entropy is computationally studied in several $1\le d \le 2$ dimensional free fermion systems that are connected by one or more point contacts (PC). For both the $k$-leg Bethe lattice $(d =1)$ and $d=2$…
We develop operator renewal theory for flows and apply this to infinite ergodic theory. In particular we obtain results on mixing for a large class of infinite measure semiflows. Examples of systems covered by our results include…
We establish the Level-1 and Level-3 Large Deviation Principles (LDPs) for invariant measures on shift spaces over finite alphabets under very general decoupling conditions for which the thermodynamic formalism does not apply. Such…
This study formulates the ideal efficiency of light-powered systems in the most general form, based on the first principle of energy-entropy flow analysis under the condition of zero entropy generation within the system. A unified formula…
In ordinary statistical mechanics the Boltzmann-Shannon entropy is related to the Maxwell-Bolzmann distribution $p_i$ by means of a twofold link. The first link is differential and is offered by the Jaynes Maximum Entropy Principle. The…
We use Arveson's notion of strongly peaking representation to generalize uniqueness theorems for free spectrahedra and matrix convex sets which admit minimal presentations. A fully compressed separable operator system necessarily generates…
In these notes we will give an overview and road map for a definition and characterization of (relative) entropy for both classical and quantum systems. In other words, we will provide a consistent treatment of entropy which can be applied…
We study dissipative dynamics constructed by means of non-commutative Dirichlet forms for various lattice systems with multiparticle interactions associated to CCR algebras. We give a number of explicit examples of such models. Using an…
Based on the mathematical model of a statistical system with scalar interaction of fermions formulated earlier, a cosmological model based on a two-component statistical system of scalar charged degenerate fermions interacting with an…